Problem: Rewrite as a simplified fraction. ${1.4\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 146.6666...\\ 10x &= 14.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 132}$ ${x = \dfrac{132}{90}} $ ${x = \dfrac{22}{15}} \text{or} {1 \dfrac{7}{15}}$